The additional damage is based on range, but I'm not 100% on the exact numbers. But according to this: http://demigod.wikia.com/wiki/Snipe  it's an extra 50 damage for every 15 yards.

It can go up to 1100ish because of the cast time and target moving further away than max range. There is also the teleport.

It probably will; however, usually it's not an issue because of the rate of healing at one's crystal.

local Projectile = import('/lua/sim/Projectile.lua').Projectile
local Buff = import('/lua/sim/buff.lua')

Bolt02 = Class(Projectile) {
    OnImpact = function(self, targetType, targetEntity)
        if(targetType == 'Unit' and targetEntity) then
            local launcher = self:GetLauncher()
            if(launcher and launcher:IsDead()) then
                launcher = targetEntity
            end
           
            # Determine Snipe's damage boost, depending on distance traveled
            # Currently: Damage +10 for every 3 traveled
            local damageperrange = 10
            local rangeblock = 3
            local targpos = table.copy(targetEntity:GetPosition())
            local launcherpos = self.DamageData.LauncherPosition
            local targetdist = VDist2(launcherpos[1], launcherpos[3], targpos[1], targpos[3])
            local damageBuff = math.floor(targetdist/rangeblock)           
            self.DamageData.Amount = self.DamageData.Amount + (damageBuff * damageperrange)
           
            if self.DamageData.Buff then
                Buff.ApplyBuff(targetEntity, self.DamageData.Buff, self.DamageData.Instigator)
            end
                     
        end
        Projectile.OnImpact(self, targetType, targetEntity)
    end,
}
TypeClass = Bolt02

10 damage every 3 yards.

Wow, Demigod's code is so clean...

Doesn't seem to be reflected in the code you posted, but some cap may exist outside the function you posted.

Also, it looks like the code allows for snipe to take any on hit damage buffs with it.  That seems consistent with my memory (You can get maimed by a snipe from regulus). It does suddenly make me wonder if things like Gloves of Fel Darkur or wyrmskin gloves can proc on a snipe.  That'd be cool:

if self.DamageData.Buff then
                Buff.ApplyBuff(targetEntity, self.DamageData.Buff, self.DamageData.Instigator)

The cap would be Snipe's range limit. Snipe's range is 90 yards. Since it gains an extra 50 damage for every 15 yards the max damage Snipe can do is 1000 at rank IV.

You're right, it's unclear if the range bonus for Snipe is determined when you target someone or after it actually hits. If it's the former then the limit is 1000 damage, but if it's the later the potential damage could be nearly twice that on larger maps.

I'll try testing it in single player, although I doubt I'll get favorable results with the AI.

I don't think crit procs WOULD effect it, but rather that things that apply buffs would. I think that's what that bit of code I wrote did. Simple to test though, are sniped targets maimed?